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    Tensorflow矩阵运算实例(矩阵相乘,点乘,行/列累加)

    栏目:代码类 时间:2020-02-05 21:11

    Tensorflow二维、三维、四维矩阵运算(矩阵相乘,点乘,行/列累加)

    1. 矩阵相乘

    根据矩阵相乘的匹配原则,左乘矩阵的列数要等于右乘矩阵的行数。

    在多维(三维、四维)矩阵的相乘中,需要最后两维满足匹配原则。

    可以将多维矩阵理解成:(矩阵排列,矩阵),即后两维为矩阵,前面的维度为矩阵的排列。

    比如对于(2,2,4)来说,视为2个(2,4)矩阵。

    对于(2,2,2,4)来说,视为2*2个(2,4)矩阵。

    import tensorflow as tf
     
    a_2d = tf.constant([1]*6, shape=[2, 3])
    b_2d = tf.constant([2]*12, shape=[3, 4])
    c_2d = tf.matmul(a_2d, b_2d)
    a_3d = tf.constant([1]*12, shape=[2, 2, 3])
    b_3d = tf.constant([2]*24, shape=[2, 3, 4])
    c_3d = tf.matmul(a_3d, b_3d)
    a_4d = tf.constant([1]*24, shape=[2, 2, 2, 3])
    b_4d = tf.constant([2]*48, shape=[2, 2, 3, 4])
    c_4d = tf.matmul(a_4d, b_4d)
     
    with tf.Session() as sess:
     tf.global_variables_initializer().run()
     print("# {}*{}={} \n{}".
      format(a_2d.eval().shape, b_2d.eval().shape, c_2d.eval().shape, c_2d.eval()))
     print("# {}*{}={} \n{}".
      format(a_3d.eval().shape, b_3d.eval().shape, c_3d.eval().shape, c_3d.eval()))
     print("# {}*{}={} \n{}".
      format(a_4d.eval().shape, b_4d.eval().shape, c_4d.eval().shape, c_4d.eval()))

    2. 点乘

    点乘指的是shape相同的两个矩阵,对应位置元素相乘,得到一个新的shape相同的矩阵。

    a_2d = tf.constant([1]*6, shape=[2, 3])
    b_2d = tf.constant([2]*6, shape=[2, 3])
    c_2d = tf.multiply(a_2d, b_2d)
    a_3d = tf.constant([1]*12, shape=[2, 2, 3])
    b_3d = tf.constant([2]*12, shape=[2, 2, 3])
    c_3d = tf.multiply(a_3d, b_3d)
    a_4d = tf.constant([1]*24, shape=[2, 2, 2, 3])
    b_4d = tf.constant([2]*24, shape=[2, 2, 2, 3])
    c_4d = tf.multiply(a_4d, b_4d)
    with tf.Session() as sess:
     tf.global_variables_initializer().run()
     print("# {}*{}={} \n{}".
      format(a_2d.eval().shape, b_2d.eval().shape, c_2d.eval().shape, c_2d.eval()))
     print("# {}*{}={} \n{}".
      format(a_3d.eval().shape, b_3d.eval().shape, c_3d.eval().shape, c_3d.eval()))
     print("# {}*{}={} \n{}".
      format(a_4d.eval().shape, b_4d.eval().shape, c_4d.eval().shape, c_4d.eval()))

    另外,点乘的其中一方可以是一个常数,也可以是一个和矩阵行向量等长(即列数)的向量。

    因为在点乘过程中,会自动将常数或者向量进行扩维。

    a_2d = tf.constant([1]*6, shape=[2, 3])
    k = tf.constant(2)
    l = tf.constant([2, 3, 4])
    b_2d_1 = tf.multiply(k, a_2d) # tf.multiply(a_2d, k) is also ok
    b_2d_2 = tf.multiply(l, a_2d) # tf.multiply(a_2d, l) is also ok
    a_3d = tf.constant([1]*12, shape=[2, 2, 3])
    b_3d_1 = tf.multiply(k, a_3d) # tf.multiply(a_3d, k) is also ok
    b_3d_2 = tf.multiply(l, a_3d) # tf.multiply(a_3d, l) is also ok
    a_4d = tf.constant([1]*24, shape=[2, 2, 2, 3])
    b_4d_1 = tf.multiply(k, a_4d) # tf.multiply(a_4d, k) is also ok
    b_4d_2 = tf.multiply(l, a_4d) # tf.multiply(a_4d, l) is also ok
     
    with tf.Session() as sess:
     tf.global_variables_initializer().run()
     print("# {}*{}={} \n{}".
      format(k.eval().shape, a_2d.eval().shape, b_2d_1.eval().shape, b_2d_1.eval()))
     print("# {}*{}={} \n{}".
      format(l.eval().shape, a_2d.eval().shape, b_2d_2.eval().shape, b_2d_2.eval()))
     print("# {}*{}={} \n{}".
      format(k.eval().shape, a_3d.eval().shape, b_3d_1.eval().shape, b_3d_1.eval()))
     print("# {}*{}={} \n{}".
      format(l.eval().shape, a_3d.eval().shape, b_3d_2.eval().shape, b_3d_2.eval()))
     print("# {}*{}={} \n{}".
      format(k.eval().shape, a_4d.eval().shape, b_4d_1.eval().shape, b_4d_1.eval()))
     print("# {}*{}={} \n{}".
      format(l.eval().shape, a_4d.eval().shape, b_4d_2.eval().shape, b_4d_2.eval()))